1. Field of the Invention
The present invention relates to digital filters, a method of generating coefficients in a digital filter system and a data carrier.
In this specification the term xe2x80x9calgorithmically stablexe2x80x9d and its inverse, instability is used. It refers to situations in which the solution to an equation becomes very sensitive to small changes in input parameters. The terms xe2x80x9cstabilityxe2x80x9d, xe2x80x9cstablexe2x80x9d and the inverses refer to such algorithmic stability and its inverse.
2. Description of the Prior Art
Background to one aspect of the present invention will now be described by way of example with reference to FIGS. 4 and 5 which are graphs showing frequency responses of illustrative filters.
It is known to provide, for example, an equalisation characteristic or EQ as shown for example in FIGS. 4 and 5. Such a characteristic can be shifted in frequency such that its peak is adjacent to the Nyquist frequency, which is half the sampling frequency of the digital filter. It is also known that currently available coefficient calculation algorithms become ill-conditioned under these conditions as will be explained hereinafter. It is desired to provide an EQ where the peak is at or even apparently beyond the Nyquist frequency.
Whilst the background to the invention has been described with reference to an EQ, the invention is not limited to EQ but may be applicable to other filter characteristics which become unstable when a portion of the characteristic is near to and/or beyond Nyquist frequency.
According to the one aspect present invention, there is provided a digital filter system, which generates a first filter characteristic which is liable to instability when a portion thereof reaches a reference frequency and which generates a second filter characteristic when the said portion of the first filter characteristic approaches its frequency zone of instability, and which second filter characteristic, substantially matches a predetermined portion of the first characteristic and is stable in the frequency zone of instability of the first characteristic.
Thus, this aspect of the invention replaces the portion below Nyquist frequency of the characteristic with a different filter characteristic which is algorithmically stable and yet which substantially matches the said portion below Nyquist frequency of the unstable characteristic. The algorithmically stable filter characteristics can be shifted to higher frequencies giving the appearance that the original EQ is operating correctly in what is in fact its region of instability.
For the example of an EQ, when the peak reaches Nyquist frequency, the portion of the EQ below Nyquist frequency resembles a portion of a shelf. In a preferred embodiment of the invention, the portion of the EQ below Nyquist frequency is replaced by a matching shelf.
According to another aspect of the invention, there is provided method of generating coefficients in a digital filter to emulate an equalisation characteristic, comprising the steps of:
(a) providing a gain control signal setting a value of peak gain G;
(b) providing a frequency control signal setting a value of centre frequency
(c) calculating, according to a model of the frequency/gain characteristic of a prototype analogue equalisation characteristic, Nyquist gain Hn, and lower half effect frequency xcfx891 and which match corresponding gain and/or frequency points in the corresponding digital filter characteristic,
(d) calculating pre-warped values xcfx89cw, xcfx891w of xcfx89c and xcfx891,
(e) calculating from Hn, G, xcfx89cw, and xcfx891w a pre-warped model of the digital filter characteristic;
(f) applying a transform to the resulting pre-warped analogue model to convert the pre-warped analogue model to the digital domain and
(g) generating filter coefficients from the transformed model and applying them to the filter.
Thus there is provided an EQ characteristic which is digitally emulated and has algorithmic stability in the Nyquist region.
Another embodiment of the invention seeks to provide a shelf digital filter which is empirically optimised to provide a good gain match in the Nyquist range with a prototype analogue filter. Another embodiment of the invention seeks to provide such a shelf which is a good match to a shelf like portion of an analogue equalisation characteristic.
According to a further aspect of the present invention, there is provided a method of generating coefficients in a digital filter, comprising the steps of:
(a) providing a gain control signal setting a value of reference gain,
(b) providing a frequency control signal setting a value of reference frequency
(c) calculating, according to a model of the frequency/gain characteristic of a prototype analogue filter, a plurality of gain and/or frequency points at frequencies equal to and less than Nyquist frequency (where Nyquist frequency is half the sampling frequency of the digital filter) and which match corresponding gain and/or frequency points in the corresponding digital filter characteristic,
(d) calculating from the said calculated points, pre-warped parameters of a model of the analogue filter,
(e) applying a transform to the resulting pre-warped analogue model to convert the pre-warped analogue model to the digital domain and
(f) generating filter coefficients from the transformed model and applying them to the filter.
In one embodiment of the invention, the analogue filter is a symmetrical shelf. In another embodiment, the analogue filter is a shelf like portion of an Equalisation characteristic.
The inventive method provides a good match in the digital domain to the desired analogue filter characteristics and maintains algorithmic stability even in the Nyquist range and allows the Equalisation characteristic to appear to have a peak beyond Nyquist frequency.
These and other aspects of the invention are specified in the claims to which attention is invited.